# Looking for a Sequence

• January 14th 2012, 08:36 AM
gotmejerry
Looking for a Sequence
Hello! Can you show me a Sequence where a_n+1 -a_n -->0 but it is not a Cauchy-sequence?
Thank you!
• January 14th 2012, 09:06 AM
CaptainBlack
Re: Looking for a Sequence
Quote:

Originally Posted by gotmejerry
Hello! Can you show me a Sequence where a_n+1 -a_n -->0 but it is not a Cauchy-sequence?
Thank you!

The harmonic series is not Cauchy (since it does not converge), now check on what happens to $a_{n+1}-a_n$ for the harmonic series.

CB